Apparently I'm in the minority, but I just can't get behind the idea of Time Lords having daemons. It makes them a little too human when HDM puts so much thematic emphasis on "has daemon = is human" and vice versa.

And the TARDISes are living beings in their own right (with their own personality and perspective, as we see several times in the Whoniverse), so making them part of their Time Lords feels really squicky to me. (Especially since the only TARDIS we really get to know is generally female-identified, and her pilot is consistently male-identified.)

That said, if they did have daemons I'm going with the "changes with every regeneration" option.